It is known to couple together two substantially identical resonant LC voltage controlled oscillators (VCO) as a unit that produces quadrature outputs. The oscillation frequency of the unit can be tuned by adjusting the coupling coefficients between the two oscillators.
FIG. 3, labeled “prior art,” is a block diagram schematic showing two coupled LC oscillators. Each has a positive feedback loop with a transfer function “Gi” between a respective input and an output coupled back to the input. The outputs of the two oscillators respectively are each coupled to a summing node at the input of the other oscillator, through a controllable coupling block. The coupling coefficients of these blocks are scalar factors m1 and m2. The outputs are shown as signals X and Y, which are to be quadrature-phase related signals at a nominal oscillation frequency.
In this arrangement, assuming steady state oscillation wherein the two oscillators are synchronized to a single oscillation frequency w, the outputs of the two oscillators must satisfy the following equations:(X+m2Y)G1(jω)=X (Y+m1X)G2(jω)=Y 
The two VCOs are identical, and can be assumed to have equal transfer functions (G1=G2=G). Further assuming equal coupling coefficients (m1=−m2=m), then it can be shown that X2+Y2=0, and therefore, X=±jY. This demonstrates that the coupled identical oscillators as shown and described produce quadrature outputs X and Y. Substituting X=±jY into one of the foregoing equations produces:(1±jm)G(jω)=1
The impedance Z(jω) of the oscillator resonator is proportional to G(jω) the gain of the oscillator stage. There are two possible oscillation frequencies, ω1 and ω2, namely whereφ(Z(jψ1))=−tan−1 m and φ(Z(jω2))=tan−1 m 
For a typical resonator with a lossy inductor having a tank arrangement as modeled in FIG. 4 (also labeled as prior art), an impedance magnitude peak occurs at a frequency higher than the resonator frequency:
      ω    0    =            1              2        ⁢        π        ⁢                  LC                      ⁢                  1        -                              CR            S            2                    L                    
Assuming that a stable oscillation is obtained at one frequency ω1 associated with the impedance peak (which inherently requires a loop gain of unity and a 180 degree phase difference), then a sustained oscillation at a second frequency ω2 is not possible because the loop gain is less than unity at frequencies other than ω1. A stable oscillation is obtained just at one frequency. Based on the foregoing equations, stable oscillation is obtained where (1+jm)G(jω)=1 and the oscillation frequency at ω1 is determined by ω(Z(jω))=−tan−1 m. These relationships suggest that the oscillation frequency of the coupled oscillators can be tuned from a frequency ω0 to a frequency ω1 as defined, by varying the coupling coefficients (m1=−m2) between zero and m. The output frequency can be tuned to a selected point in a frequency range by varying the coupling coefficient between the two LC oscillators (i.e., by varying the absolute value of the coupling coefficient up to a maximum m).
The frequency tuning range is determined by the phase-frequency characteristics of G(jω) and by the range of deviation of the coupling coefficient m. An upper bound of m is reached at a limit resulting from phase noise performance. A lower bound of m is reached due to a multi-mode oscillation phenomenon. In practice it is not possible to have two perfectly-matched oscillators. Each oscillator will have a slightly different natural oscillation frequency (i.e., when no coupling is applied). If the extent of coupling (m) is made smaller and smaller, a point is reached when the coupling becomes too weak to prevent the oscillators from seeking their different natural frequencies, giving rise to a multi-tone output signal as a result of nonlinear limiting in the feedback loops. The minimum value of the coupling coefficient m is a function of the extent of mismatch between G1 and G2.
Generally, the aim of an LC oscillator of this type (i.e., either single LC oscillator as opposed to the coupled pair) is to provide NMOS and/or PMOS cross coupled transistor pairs that switch between conducting and nonconducting states at a frequency determined by the resonant tank circuit. The pairs are arranged so as to shift currents back and forth between capacitive and inductive elements in a complementary way. Some energy is lost in every cycle, including energy dissipated in parasitic resistances of the LC tank. As a result, an LC resonator by itself could not maintain steady oscillation over time. However, in an appropriate configuration, cross-coupled differential transistors can provide the negative resistance necessary to replenish the energy that is lost. Oscillation can continue indefinitely.
In order to provide stable oscillation, the negative resistance (or transconductance) of such an oscillator must cancel out the energy dissipated by the resonant LC tank. To ensure start-up oscillation, transconductances are advantageously chosen to be two or three times the minimal acceptable value. To provide transconductance as necessary, the VCO necessarily dissipates a current. The serial current through each VCO is known as the VCO “tail current.” The transconductance value is proportional to the square-root of the tail current.
In the cross coupled oscillator stage described above, the tuning elements that control the coupling coefficients between the two stages (m1=−m2) between zero and m, likewise require bias and contribute to the current load on the power supply. The bias on the coupling and switching controls produces a bias current that can be termed the coupling circuit tail current.
In a known VCO unit described in “A 6.5 GHz monolithic CMOS voltage controlled oscillator,” Liu T. P., et al., ISSCC, February, 1999, pp. 404-405, a technique is disclosed wherein transistor elements vary the extent of coupling between two VCO stages, for tuning the frequency of the coupled pair. A control voltage is applied to the transistor coupling elements for obtaining a selected coupling coefficient in a tuning range. The VCO tail currents of the coupled oscillators are equal because the oscillators are equal (insofar as practically possible). The tail currents dissipated by two couplers are equal because the coupling coefficients have equal absolute values (m1=−m2). As discussed in Liu T. P.'s paper, the coupling coefficient m=(I1/I0)n, where I1 is the coupler tail current, I0 is the VCO tail current, and n=0.5 to 1.0. In the Liu paper, I1 is tuned; and I0 remains constant. The coupling elements may carry more or less coupling circuit tail current, depending on the point at which the circuit happens to be tuned in its operational range. The VCO tail currents and the coupling circuit tail currents both load the power supply. Under tuning conditions where the coupling circuit tail current is high, the sum of the constant VCO tail current and the variable coupling circuit tail current may be such that the device dissipates considerable power.
What is needed is a way to control oscillation frequency that is similarly convenient, i.e., by controlling the driving current applied to coupling components, without suffering undue tail current dissipation in the steady state and/or at any particular operational state over a tuning range.